Water and hydroxyl, once thought to be found only in the primitive airless bodies that formed beyond roughly 2.5-3 AU, have recently been detected on the Moon and Vesta, which both have surfaces dominated by evolved, non-primitive compositions. In both these cases, the water/OH is thought to be exogenic, either brought in via impacts with comets or hydrated asteroids or created via solar wind interactions with silicates in the regolith or both. Such exogenic processes should also be occurring on other airless body surfaces. To test this hypothesis, we used the NASA Infrared Telescope Facility (IRTF) to measure reflectance spectra (2.0 to 4.1 μm) of two large near-Earth asteroids (NEAs) with compositions generally interpreted as anhydrous: 433 Eros and 1036 Ganymed. OH is detected on both of these bodies in the form of absorption features near 3 μm. The spectra contain a component of thermal emission at longer wavelengths, from which we estimate thermal of 167±98 J m−2s−1/2K−1 for Eros (consistent with previous estimates) and 214±80 J m−2s−1/2K−1 for Ganymed, the first reported measurement of thermal inertia for this object. These observations demonstrate that processes responsible for water/OH creation on large airless bodies also act on much smaller bodies.